Testing Stationarity in Sector-to-Market Correlations

Summary

The document describes an analysis of daily returns for eleven MSCI World sectors and the MSCI ACWI index. The analyst groups daily observations into weekly and monthly periods, calculates a correlation for each group, and applies the Augmented Dickey-Fuller test to each resulting correlation series. The reported stationarity conclusions differ between the weekly and monthly versions, prompting questions about which aggregation is preferable and what further tests could help.

The excerpt does not include the underlying correlation series, test statistics, or test specifications, so it offers no basis for choosing one frequency or interpreting the reported outcomes. A key limitation is that each weekly correlation is estimated from only a handful of daily observations, while monthly estimates also rely on relatively short samples; these noisy estimates can affect unit-root tests. The choice of aggregation should follow the research question and be supported by diagnostics for serial dependence, window sensitivity, and structural changes. The Augmented Dickey-Fuller test evaluates a unit-root null under its modeling assumptions, but alone it does not establish that correlations are stable or economically useful.

Key ideas

• The analysis compares weekly and monthly sector-to-index correlation series using Augmented Dickey-Fuller tests.
• Different aggregation frequencies can produce different stationarity conclusions.
• Correlations estimated from very few daily observations may be noisy and complicate unit-root testing.
• The excerpt omits test settings, numerical results, and the series needed to assess its findings.
• Stationarity tests alone do not establish stable dependence or its usefulness for investment decisions.

Tags

# Correlation between a sector and MSCI ACWI returns


# Correlation between a sector and MSCI ACWI returns












I have daily return data of 11 sectors of MSCI World Index and the MSCI ACWI index. I want to know the stationarity of correlations between the sectors and MSCI ACWI index.

This is what I have done:

1) aggregate the daily returns into month and calculate correlation between each of the sectors and the MSCI ACWI index (so for each monthly correlation, around 20 daily returns were used). Then I used the Augmented Dickey-Fuller test to see if the monthly correlation time series is stationary or not.

2) aggregate the daily returns into week and calculate correlation between each of the sectors and the MSCI ACWI index (so for each weekly correlation, around 5 daily returns were used). Then I used the Augmented Dickey-Fuller test to see if the weekly correlation time series is stationary or not.

The result is reproduced here:

As you can see, the stationary result is different for monthly and weekly correlations.

My question is:

1) which model is a better one?

2) what other kinds of tests or useful stuff can I do with this stationary test?

Thank you in advance!

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.